Knowledge of the extent and range of linkage disequilibrium (LD), defined as non-random association of alleles at two or more loci, in animal populations is extremely valuable in localizing genes affecting quantitative traits, identifying chromosomal regions under selection, studying population history, and characterizing/managing genetic resources and diversity. Two commonly used LD measures, r 2 and D', and their permutation based adjustments, were evaluated using genotypes of more than 6,000 pigs from six commercial lines (two terminal sire lines and four maternal lines) at ~4,500 autosomal SNPs (single nucleotide polymorphisms). The results indicated that permutation only partially removed the dependency of D' on allele frequency and that r 2 is a considerably more robust LD measure. The maximum r 2 was derived as a function of allele frequency. Using the same genotype dataset, the extent of LD in these pig populations was estimated for all possible syntenic SNP pairs using r 2 and the ratio of r 2 over its theoretical maximum. As expected, the extent of LD highest for SNP pairs was found in tightest linkage and decreased as their map distance increased. The level of LD found in these pig populations appears to be lower than previously implied in several other studies using microsatellite genotype data. For all pairs of SNPs approximately 3 centiMorgan (cM) apart, the average r 2 was equal to 0.1. Based on the average population-wise LD found in these six commercial pig lines, we recommend a spacing of 0.1 to 1 cM for a whole genome association study in pig populations.
Efficient haplotyping in pedigrees is important for the fine mapping of quantitative trait locus (QTL) or complex disease genes. To reconstruct haplotypes efficiently for a large pedigree with a large number of linked loci, two algorithms based on conditional probabilities and likelihood computations are presented. The first algorithm (the conditional probability method) produces a single, approximately optimal haplotype configuration, with computing time increasing linearly in the number of linked loci and the pedigree size. The other algorithm (the conditional enumeration method) identifies a set of haplotype configurations with high probabilities conditional on the observed genotype data for a pedigree. Its computing time increases less than exponentially with the size of a subset of the set of person-loci with unordered genotypes and linearly with its complement. The size of the subset is controlled by a threshold parameter. The set of identified haplotype configurations can be used to estimate the identity-by-descent (IBD) matrix at a map position for a pedigree. The algorithms have been tested on published and simulated data sets. The new haplotyping methods are much faster and provide more information than several existing stochastic and rule-based methods. The accuracies of the new methods are equivalent to or better than those of these existing methods.
A maximum likelihood method is presented that can be used to construct parental haplotypes based on their progeny genotypes. The exact error rate and choice of family size in haplotype construction were evaluated through mathematical expressions and numerical examples. Numerical results suggest that, if two markers are tightly linked (< or = 10 cM) and each has intermediate allele frequencies, a difference of one between progeny receiving parental and recombinant gametes is sufficient for constructing sire linkage phase; a difference of two or more progeny is required with two markers 30 cM apart. When each of two adjacent markers has two alleles with equal allelic frequencies, genotyping 10 and 50 progeny are needed to achieve a power of 0.85 for constructing a sire linkage phase of two tightly (10 cM) and moderately tightly linked (30 cM) markers, respectively. The family size is reduced by approximately half when both markers have three alleles with equal frequencies. Results suggest that, when an experiment requiring haplotype determination of a parent is being designed, researches should choose the appropriate threshold and family size in the context of marker allelic frequencies and recombination fractions.
Daughter and granddaughter half-sib designs for mapping quantitative trait loci were modified to increase experimental power. This new design includes a two-stage procedure, in contrast to conventional one-step half-sib designs. In stage 1, a few progeny of each sire are genotyped for marker loci. Based on the analyses of stage 1 data, some sires are chosen to continue genotyping more progeny for stage 2. When multiple chromosomes are under investigation, chromosomes and sires for stage 2 are selected based on the analysis of stage 1 data. Sire selection results in increased frequency of heterozygous genotypes of interest in stage 2 if the markers are linked to those genes. Chromosome selection can increase the proportion of chromosomes with segregating quantitative trait loci in stage 2 if not all of the chromosomes evaluated in stage 1 have segregating quantitative trait loci. Numerical results indicated that two-stage half-sib designs are generally more powerful than conventional designs when 1) the noncentrality parameter is moderate or larger, 2) larger quantitative trait loci are mapped using tightly linked markers in larger families, and 3) variation is large in numbers and sizes of segregating quantitative trait loci among the chromosomes evaluated in stage 1.
Choosing families to sample for a quantitative trait locus mapping experiment is a critical component of experimental design because only heterozygous families contribute information to the analysis. Additive genetic variance of a paternal half-sib family can be partitioned into two parts: a variance component of maternal source that is constant across different families and a variance component of paternal source that is defined as an index of heterozygosity of a sire. This index is shown to be an upper limit of variance among marker genotypes of a half-sib family and can be used to identify highly heterozygous sires, thus improving the power of detecting QTL in detection studies. Simulated progeny phenotypic data were used to estimate sire's heterozygosity index via an ANOVA method, and accuracy of the estimation was evaluated with the correlation coefficient between the true and estimated index summarized both as the correlation and by the correct ranking of results as measured by the ratio of the true average heterozygosity index of experimentally selected parents to average heterozygosity of all sires. Positive but small correlation can be achieved in the estimation of a sire's heterozygosity when based on the daughters' phenotypic data, and accuracy was improved when progeny-tested sons were used to estimate their grandsire's heterozygosity index, depending on the genetic model of a trait and the size and structure of families.
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